The key factor that you left out is how high the tip of the pole is above the mast step.

I went through this process a few months ago. You can rough-calculate this with trig, but there's a lot of variables that you won't know until you actually rig the boat.

My solution was to fake-rig the boat. Put a 12' pole on the boat - doesn't need to be a real spin pole, just something nice and straight. Make sure it's attached to the boat like the real pole will be, including pre-bend.

Then, with the mast up, actually measure the distance from where you want the spin tang to be to the tip of the spin pole. You can use a piece of line to do this. Use a fairly heavy piece of line (not kite string) as you'll need to put some tension on it to keep it straight and you don't want it to stretch too much.

For extra credit, if you also measure the distance from somewhere else on the mast (such as the hounds) to the pole tip, you can calculate the luff length for any tang position on the mast fairly easily using the law of cosines. That way you can figure out where the tang will need to be for a specific luff length.